Question:

​What can you say about the prime factorisations of the denominators of the following rationals:

(i) 43.123456789

(ii) $43 . \overline{123456789}$

(iii) $27 . \overline{142857}$

(iv) 0.120120012000120000 ...

Solution:

(i) Since 43.123456789 has terminating decimal expansion.

So, its denominator is of the form 2m × 5n, where mn are non-negative integers.

(ii) Since $43.123456789$ has non-terminating decimal expansion.

 

So, its denominator has factors other than 2 or 5 .

(iii) Since $27 . \overline{142857}$ has non-terminating decimal expansion.

 

So, its denominator has factors other than 2 or 5 .

(iv) Since $0.120120012000120000 \ldots$ has non-terminating decimal expansion.

 

So, its denominator has factors other than 2 or 5 .

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now